UCLA STATS 13 - Lecture Notes (8 pages)

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Lecture Notes



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Lecture Notes

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Lecture Notes


Pages:
8
School:
University of California, Los Angeles
Course:
Stats 13 - Introduction to Statistical Methods for Life and Health Sciences
Introduction to Statistical Methods for Life and Health Sciences Documents

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UCLA STAT 13 Introduction to Statistical Methods for Chapter 5 Discrete Random Variables the Life and Health Sciences zRandom variables Ivo Dinov zInstructor zProbability functions Asst Prof In Statistics and Neurology zThe Binomial distribution zTeaching Assistants Tom Daula and Kaiding Zhu UCLA Statistics zExpected values University of California Los Angeles Fall 2002 http www stat ucla edu dinov Slide 1 STAT 13 UCLA Ivo Dinov Slide 2 STAT 13 UCLA Ivo Dinov Definitions Definitions z An experiment is a naturally occurring phenomenon a scientific study a sampling trial or a test in which an object unit subject is selected at random and or treated at random to observe measure different outcome characteristics of the process the experiment studies z The probability function for a discrete random variable X gives P X x denoted pr x or P x for every value x that the R V X can take z E g number of heads when a coin is tossed twice x z A random variable is a type of measurement taken on the outcome of a random experiment Slide 3 possible outcomes from this experiment 1 8 Probability 1 8 GB BG BBG BBB 1 4 1 4 1 8 1 8 0 1 pr x 1 8 5 8 Slide 5 2 1 8 STAT 13 UCLA Ivo Dinov X 0 1 pr x 1 8 5 8 2 1 8 3 1 8 P X 75 50 z For R V X number of girls we have X 2 1 4 Plotting the probability function Sample Space complete unique description of the GGG GGB 1 1 2 Slide 4 STAT 13 UCLA Ivo Dinov Stopping at one of each or 3 children Outcome 0 1 4 pr x 3 1 8 STAT 13 UCLA Ivo Dinov 25 0 1 2 Slide 6 3 X STAT 13 UCLA Ivo Dinov 1 Tossing a biased coin twice Hospital stays z For each toss P Head p P Tail P comp H 1 p z Outcomes HH HT TH 4 5 6 7 8 9 10 Total x Frequency 10 30 113 79 21 8 2 263 Proportion pr X x 0 038 0 114 0 430 0 300 0 080 0 030 0 008 1000 Cumulative pr X x 0 038 0 152 0 582 0 882 0 962 0 992 1 000 Proportion Days stayed TT z Probabilities p p p 1 p 1 p p 1 p 1 p z Count X the number of heads in 2 tosses X pr x 0 1 p 2 1 2p 1 p Slide 7 From Chance Encounters by C J Wild and G A F



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